As you said that the Twitter account is still new and upon seeing the account it only had 18 followers right now, so I guess advertising using that account is not good enough even if you said it's free but the backlinking method of sites will do good about it. Then I hope someone will try this free advertising of yours.
I agree, the twitter has no audience and that will mean even if this was a free service it would really do anything but post it on a useless twitter account. What's good though, is that there is nothing to lose for both parties here. Though, there is also nothing to gain.
